Talk:Hagen–Poiseuille flow from the Navier–Stokes equations

Hagen-poiseuille equation;

$\Delta P=(32\mu vL)/D^{2}$

See equation 7 of Three approaches to calculating the velocity profile of a laminar incompressible fluid flow in a hollow tube

C. Neipp1, A. Hernández1, T. Beléndez2, J. J. Rodes1, and A. Beléndez1 1Departamento de Física, Ingeniería de Sistemas y Teoría de la Señal, Universidad de Alicante, E-03080 Alicante, Spain 2Departamento de Ciencia y Tecnología de los Materiales, Universidad Miguel Hernández de Elche, Avda. del Ferrocarril, s/n. E-03202 Elche Alicante, Spain

link http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000071000001000046000001&idtype=cvips&doi=10.1119/1.1517596&prog=normal

the other steps are correct ( I think)

Jgreeter (talk) 02:35, 5 May 2011 (UTC)

I do not see anything wrong with the 'equation for pressure drop' provided in the article. Please explain if you found it incorrect. Salih (talk) 03:51, 5 May 2011 (UTC)

Pressure gradient

"Assuming that the pressure decreases linearly across the length of the pipe, we have $-{\frac {\partial p}{\partial z}}={\frac {\Delta p}{L}}$ (constant)"

This sentence is actually imprecise. By the z-component of the equation of motion

${\frac {1}{r}}{\frac {\partial }{\partial r}}\left(r{\frac {\partial u_{z}}{\partial r}}\right)={\frac {1}{\mu }}{\frac {\partial p}{\partial z}}$ ,

indeed, the pressure gradient must be constant, since – by incompressibility – the left-hand side is a function of $r$ only, and the right-hand side is a function of $z$ only. — Preceding unsigned comment added by Aspro89 (talk • contribs) 12:29, 4 December 2017 (UTC)